Wet clutches are known that have friction linings in which embossing is provided. Such embossing is produced by pressing a profiled die onto the surface during the manufacturing process. In the area of a raised profile of the die, the porous material of the friction lining is more severely compressed than on non-profiled surfaces. That results in a friction lining that exhibits grooves at the more severely compressed places and has no porosity in the area of these grooves, i.e. is impervious. The grooves are provided to carry a stream of oil for cooling from an outer side across the lining to a radially inner side of the friction lining when the wet clutch is engaged, so that in the area of the grooves a cooling effect results on the lining and on the adjacent opposing friction surface. Because of the deformation of the friction lining in the area of the grooves, transporting of cooling oil through the pores of the friction lining is no longer possible at these places; the thermally insulating properties of the friction lining make cooling these areas difficult. This makes a relatively high flow volume of cooling oil necessary, and the large proportion of the surface taken up by the necessary grooves is very high in comparison to the effective friction surface.